Conversions between barycentric, RKFUN, and Newton representations of rational interpolants

TL;DR

This paper develops explicit formulas for converting between barycentric, RKFUN, and Newton forms of rational interpolants, facilitating their use in rational approximation and eigenvalue problems.

Contribution

It introduces new explicit conversion formulas between different rational interpolant representations, enhancing computational flexibility and application scope.

Findings

Derived explicit formulas for conversions between representations

Enabled improved use of rational approximants in eigenvalue problems

Facilitated integration with the AAA algorithm and Rational Krylov Toolbox

Abstract

We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. S\`ete, L. N. Trefethen, arXiv preprint 1612.00337, 2016] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems.